Look, I love The Police. But IMO, “new wave” comes with the expectation that a song is new and different, perhaps edgy, and features some synth or guitar effects. Don’t Stand So Close To Me was a great choice.
There’s nothing wrong with King of Pain or Every Little Thing She Does Is Magic. They are good songs. But to my ears, they are much closer to pop songs and ballads than they are new wave songs, ESPECIALLY when The Police have plenty of new wave songs in their own right.
Again IMO, either Synchronicity 1 or 2 are more new wave. If we had to go with a slower song, Wrapped Around Your Finger. as the sound is different than most other songs of the era. Pretty much any other song on Ghosts In The Machine would be more of a new wave option than ELTSDIM. But again, not knowing what else is on the list makes it harder to criticize or comment. Carry on. Don’t want to be a buzz kill.